Forces created by the proliferation of computer hardware and software, by innovative methods of mathematical modelling and applications, by broader demographic considerations, and by schools themselves are profoundly changing the way mathematics is practiced, the way mathematics is taught, and the way mathematics is learned. In this volume, a vision of the richness of mathematics is expressed and illustrated as five different possible strands of school mathematics through the expansion on the theme of mathematics as the language and science of patterns with emphases on interconnections and communalities. Included are: (1) an introduction to the five sample strands with examples of the continuity underlying the fundamentals of mathematics, of the mathematical connections that both unite and repeat, and of the mathematical perspective necessary to view both the variety and the regularity of patterns; (2) the Dimension strand, which focuses on the development of relationships between the different dimensions with emphasis on three-dimensional topics; (3) the Quantity strand, which provides insights into the three basic tasks of measuring, ordering, and coding with attendant symbologies and procedures; (4) the Uncertainty strand, which develops ideas about the natural themes and strategies within the twin concepts of data and chance; (5) the Shape strand, which uses classification to discover similarities and differences among objects, analysis to discern the components of form, and representation to recognize and comprehend shapes within different contexts; and (6) the Change strand, which advocates imaginative and sensitive responses to the constantly emerging new types of patterns, including patterns of thinking about nature, as well as mathematics. (31 references) (JJK)